Question: Simplify the following expression: $ a = \dfrac{-8}{-3n - 7} + \dfrac{-8}{3} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{-8}{-3n - 7} \times \dfrac{3}{3} = \dfrac{-24}{-9n - 21} $ Multiply the second expression by $\dfrac{-3n - 7}{-3n - 7}$ $ \dfrac{-8}{3} \times \dfrac{-3n - 7}{-3n - 7} = \dfrac{24n + 56}{-9n - 21} $ Therefore $ a = \dfrac{-24}{-9n - 21} + \dfrac{24n + 56}{-9n - 21} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-24 + 24n + 56}{-9n - 21} $ $a = \dfrac{24n + 32}{-9n - 21}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{-24n - 32}{9n + 21}$